1. Are X and Y independent? NO
2. Find fX(x). Express your answers in terms of x using standard notation .
If 0<x<1,
fX(x)= x/2
If 1<x<2,
fX(x)= -3*x/2+3
Find fY|X(y∣0.5).
If 0<y<1/2,
fY|X(y∣0.5)= 2
3. Find fX|Y(x∣0.5).
If 1/2<x<1,
fX|Y(x∣0.5)= 0.5
If 1<x<3/2,
fX|Y(x∣0.5)= 1.5
Let R=XY and let A be the event {X<0.5}. Evaluate E[R∣A].
E[R∣A]= 0.0625
Answered in full...
This figure below describes the joint PDF of the random variables X and Y. These random variables take values in [0,2] and [0,1], respectively. At x=1, the value of the joint PDF is 1/2.
Are X and Y independent?
- unanswered Yes No
Find fX(x). Express your answers in terms of x using standard notation .
If 0<x<1,
fX(x)= - unanswered
If 1<x<2,
fX(x)= - unanswered
Find fY|X(y∣0.5).
If 0<y<1/2,
fY|X(y∣0.5)= - unanswered
Find fX|Y(x∣0.5).
If 1/2<x<1,
fX|Y(x∣0.5)= - unanswered
If 1<x<3/2,
fX|Y(x∣0.5)= - unanswered
Let R=XY and let A be the event {X<0.5}. Evaluate E[R∣A].
E[R∣A]= ??
1 answer
2 answers